Ask The Wizard #151

Your strategy cards for Blackjack I presume is basic strategy for the initial cards (player's first two cards and dealer's up card). However, after hitting or splitting the deck composition has changed and the basic strategy may have changed. What I think would be more appropriate is a basic strategy based on the overall game of blackjack, including after splitting and hitting. Is there any situation where your initial hand basic strategy and one for the overall game are different?

Arian from Luton

Yes, my basic strategy charts are designed to be the best play based on the first two cards. This is the usual approach to developing the basic strategy. One benefit to this approach is the expected values of each play can be calculated exactly and compared to other sources. However, you bring up a valid point. So I asked Don Schlesinger, author of Blackjack Attack, if there were any known play where the best play on the initial hand is different from the best play to maximize the expected value of the overall game of blackjack. He replied that a soft 18 against a dealer ace, in a double-deck game, where the dealer stands on soft 17, was such a play. As my blackjack appendix 9 shows the expected value for standing is -0.100502 and for hitting is -0.100359. So, based on the first two cards, the odds favor hitting by 0.000143. However, there are many more ways to see soft 18 than one ace and one seven. The following table shows all the ways this hand can turn up.

Soft 18 Vs Ace Combinatorial Analysis

A7 0.621139169 -0.100359 -0.100502 -0.062336906 -0.062425729
A6A 0.036728229 -0.11202 -0.116009 -0.004114296 -0.004260805
A52 0.146912917 -0.111299 -0.103382 -0.016351261 -0.015188151
A43 0.146912917 -0.114804 -0.103721 -0.01686619 -0.015237955
A5AA 0.001827682 -0.111395 -0.105122 -0.000203595 -0.00019213
A42A 0.016814677 -0.116975 -0.108233 -0.001966897 -0.001819903
A33A 0.007356421 -0.132142 -0.107256 -0.000972092 -0.00078902
A322 0.020470041 -0.134229 -0.11004 -0.002747673 -0.002252523
A4AAA 0.000073486 -0.117554 -0.110984 -0.000008639 -0.000008156
A32AA 0.001028802 -0.134775 -0.112433 -0.000138657 -0.000115671
A222A 0.000709873 -0.136788 -0.114993 -0.000097102 -0.00008163
A3AAAA 0.000002238 -0.135313 -0.114821 -0.000000303 -0.000000257
A22AAA 0.000023502 -0.137312 -0.117376 -0.000003227 -0.000002759
A2AAAAA 0.000000046 -0.137859 -0.119823 -0.000000006 -0.000000006
Total 1 -0.105806844 -0.102374694

Explanation of column titles

Player cards:Cards in player’s hand
Conditional probability: Given that the player has a soft 18 against a dealer ace the probability of the given hand composition.
Hit EV:Expected value by hitting
Stand EV:Expected value by standing
Hit Return:Product of probability and hit expected value
Stand Return:Product of probability and stand expected value

The right two cells of the bottom row show that overall the expected value of hitting is -0.105807 and for standing is -0.102375. So, the table shows the odds favor standing by 0.00343.

To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play. I counted only hands where soft 18 against a dealer ace happened at any time during play. Here are my results.

Soft 18 Vs Ace Simulation

Soft 17 Hands
Stand 3857490 -396224 -0.102715
Hit 3208390 -337572 -0.105215

So, the simulation shows the odds favor standing by 0.0025 over all possible scenarios where this hand turns up. Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.

I am a German student and I was looking for a casino article ranking the world’s best 100 casinos (real world), but I couldn’t find any. I hope you can help me with my question.

Mathias from Berlin, Germany

The Ultimate Casino Guide has various top ten lists. Here is their list of the ten most elegant casinos in alphabetical order.

  • 50 St. James, London, England
  • Atalantis at Paradise Island, Nassau, Bahamas
  • Casino Baden-Baden, Germany
  • Casino Bellevue Marienbad, Czech Republic
  • Casino de Montreal, Montreal Quebec
  • Le Casino, Monte Carlo
  • St. James Club, Antigua
  • Taleon Club, Saint Petersburg, Russia
  • Venetian, Las Vegas, Nevada

My boyfriend and I have been dating on and off for two years. We have a child together and have been living together for the last 5 months. It frustrates me that my boyfriend, right after coming home from work, goes to the gym for 3 hours about twice a week. I have nagged and complained saying that is doesn’t take 3 hours to go to the gym. He always goes with his one buddy and my suspicion is that they’re doing more than going to the gym. Tonight he’s working late---conveniently he told me that he told his boss that he’ll work three hours overtime and no more. Do I have the monkey by the tail or is there something up? What can he possibly doing for three hours two times a week?? Thank you in advance for your time, Regards,

Tifanny from Vancouver

Three hours at the gym sounds fishy to me too, not to mention working overtime the same amount of time. If he is cheating then nagging him with circumstantial evidence will not make him stop. It will just make him try harder to avoid detection. My advice is act like you believe him and hire a private investigator to tail him. You want him to have his guard down, he will be easier to catch that way. If it turns out you’re right get as far away from the bum as possible. Until then you don’t have enough evidence to be making any accusations.

Hi, fantastic site, keep up the good work :) I’m trying to work out risk of ruin statistics for any given combination of number of betting units and number of hands to play. Currently if the pair of values don’t appear in your RoR [Risk of Ruin] table in the blackjack appendix then I have no accurate percentage chance of ruin. Would you publish the formula for us please? Many thanks.

Hector from Cardiff, UK

Thanks. I explain how I calculate the risk of ruin in video poker in my video poker appendix 1. However for games where the bet amount is not always the same the calculations get very messy and computer simulations are necessary.

At Bally’s in Atlantic City there’s 1$ 9/6 JoB [Jacks or Better] video poker with a progressive royal flush payout beginning at 4k. Since non progressive 9/6 JoB have a return of 99.54% with perfect play, at which point would the progressive payout raise the return above 100%?


My Jacks or Better section shows the return of a 940/9/6 game to be 0.999030. The return from the royal is 0.024686. So the return from the other hands must be 0.999030-0.024686 = 0.97434. Although the probability of a royal is shown as 0.000026, that is only to two significant digits. Let’s use the return divided by the win, or 0.024686/940 as the probability. If j is the jackpot amount solve for j in the following equation:

1=0.97434 + j*(0.024686/940)
j = (1-0.97434)/(0.024686/940) = 977.33182.

So the breakeven point is a meter of 977.33 bet units or $4886.66. This assumes perfect 940/9/6 strategy. However few people know 940/9/6 strategy. If using 800/9/6 strategy then we would use the 800/9/6 table:

1 = (0.99543904-0.01980661) + j*(0.01980661/800)
j = (1 - (0.99543904-0.01980661))/(0.01980661/800)
j = 984.2197

So if using 800/9/6 strategy the jackpot would need to reach 984.22 bet units or $4921.10.

How can I prove an Internet casino is cheating at blackjack?

Ed from Indianapolis

As I’ve said before you need to gather some evidence. If you’re not sure how they are cheating then a simple tally of total initial bets made and units lost will suffice. You should flat bet one hand at a time, play perfect basic strategy, and do not count money bet doubling and splitting towards number of bets made. If based on your results the probability of your losses are less than 1 in 10,000 I think there is reason to be suspicious, and would be interested in seeing your evidence so that I may try to corroborate it. Based on a house edge of 0.5% and a standard deviation of 1.15 here is how much you need to be down according to the number of hands. This is based on total hands played since you started keeping track.

0.01% Losing Percentile in Blackjack

Hands Net Loss
100 43
200 61
500 98
1000 140
2000 201
5000 327
10000 478
The formula for being down x units of y hands played is shown in my FAQ.

Why do casinos predominately use green felt for their layouts? Has there been a study on this and if so where can I look for the results?

Carol from Reno

I asked Barney Vinson, author of Ask Barney: An Insider’s Guide to Las Vegas this question. He speculated it is a carry-over from the days of illegal gambling, but had no idea why the illegal tables used green felt. This is just a theory but I believe it is because pool table felt is usually green. The makers of gambling tables probably found green felt in the greatest supply because of the abundance of pool tables. However that begs the question, why do pool tables use green felt? I did some searching and found this explanation:

"The History of billiards is long and very rich. The game has been played by kings and commoners, presidents, mental patients, ladies, gentlemen, and hustlers alike. It evolved from a lawn game similar to the croquet played some-time during the 15th century in Northern Europe and probably in France. Play moved indoors to a wooden table with green cloth to simulate grass, and a simple border was placed around the edges." - Dolly’s Pro Shop

Hey, i really appericate you doing this thanks. Now to my question. I used to know this girl in high school. we used to be friends. After it was about to end i liked her but never thought she would like me so didnt do nothing. 3 yrs later, now. she found me on a website. She was so happy ans send me a friends request and a message saying how happy she was finding me. I accepted it and she gave me her screen name so we can talk. So we talked and it was all good and she kept saying im happy i found you. Then she asked me if i ever had a crush on me. and i said u go 1st and she said yes i did, then i told her also i did. and it was good from there and felt like she really did like me. Then after a few days. she stopped talking to me as often then she used to. Doesnt write as much emails and doesnt talk to me like before and i feel like she doesnt like me no more like she forgot me. I dont know what happen. What do you think? What should i do?

Andrew from New York City

You put each other on the spot with this question, which is almost always a big mistake. Maybe she just wanted to satisfy her curiosity or get a boost to her self-esteem from your confession. After the smoke cleared there was no mystery any longer. So I think she is lowering the temperature because she has no use for you any longer. My advice is let it go.